Such a vacuum switch is known from DE-OS 3544972. A vacuum switch chamber is arranged in a cylindrical housing made of insulating material. Above this vacuum switch chamber a connecting element is provided, the clamping part of which, arranged inside the housing, embraces and clamps a connecting spigot, projecting in the axial direction, of the vacuum switch chamber. This clamping part is bolted to a connecting bolt which passes through the housing in the radial direction through a corresponding passage. At the end furthest away from the connecting bolt, the clamping part has a spigot which engages in a blind hole-like recess, diametrically opposite the passage, in the housing. The connecting bolt which is introduced from the outside into the passage is constructed to be flange-like and is bolted from the outside to the housing. When mounting the vacuum switch, the switch chamber is introduced eccentrically into the housing from above together with the clamping part premounted on it and is aligned in such a way that, when the spigot is subsequently centered, it comes to rest in the recess. The connecting bolt is then pushed through the passage in a radial direction from the outside and bolted to the clamping part and to the housing. This known vacuum switch is costly in terms of construction and mounting and requires the housing to have an inner diameter which allows the eccentric introduction of the clamping part together with the vacuum switch chamber.